Question

5 si 6
Dau coroana si 28 de puncte.
Materie clasa a 10-a.
Multumesc anticipat.​

Answer 1

$\it\ 5)\ (BC):\ \dfrac{x-x_B}{x_C-x_B} = \dfrac{y-y_B}{y_C-y_B} \Rightarrow \dfrac{x+1}{2+1} = \dfrac{y-2}{-2-2} \Rightarrow \dfrac{x+1}{3} = \dfrac{2-y}{4} \Rightarrow \\ \\ \\ \Rightarrow 4x+4=6-3y \Rightarrow 4x+3y-2=0\\ \\ \\ d(O,\ BC) = \dfrac{|-2|}{\sqrt{4^2+3^2}} = \dfrac{2}{5}=0,4$

$\it 6)\ a\in \Big( \dfrac{\pi}{2},\ \pi \Big) \Rightarrow cosa< 0\\ \\ cosa=-\sqrt{1-sin^2a}=-\sqrt{1- \dfrac{9}{25} }=-\sqrt{ \dfrac{16}{25} }=- \dfrac{4}{5} \\ \\ \\ ctga= \dfrac{cosa}{sina}= \dfrac{- \dfrac{4}{5} }{ \dfrac{3}{5} } =- \dfrac{4}{3}$